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Vivien Loo, Guillaume Blanquer, Maxime Joos, Quentin Glorieux, Yannick de Wilde, Valentina Krachmalnicoff
To cite this version:
Vivien Loo, Guillaume Blanquer, Maxime Joos, Quentin Glorieux, Yannick de Wilde, et al.. Imaging
light scattered by a subwavelength nanofiber, from near field to far field. Optics Express, Optical
Society of America - OSA Publishing, 2019, 27 (2), pp.350-357. �10.1364/oe.27.000350�. �hal-02024985�
Imaging light scattered by a subwavelength nanofiber, from near field to far field
V IVIEN L OO , 1 G UILLAUME B LANQUER , 1 M AXIME J OOS , 2 Q UENTIN G LORIEUX , 2 Y ANNICK D E W ILDE , 1 AND V ALENTINA
K RACHMALNICOFF 1,*
1
Institut Langevin, ESPCI Paris, CNRS, PSL University, 1 rue Jussieu, 75005 Paris, France
2
Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL University, Collège de France, Paris 75005, France
*valentina.krachmalnicoff@espci.fr
Abstract: We present a direct experimental investigation of the optical field distribution around a suspended tapered optical nanofiber by means of a fluorescent scanning probe. Using a 100 nm diameter fluorescent bead as a probe of the field intensity, we study interferences made by a nanofiber (400 nm diameter) scattering a plane wave (568 nm wavelength). Our scanning fluorescence near-field microscope maps the optical field over 36 µ m
2, with λ/ 5 resolution, from contact with the surface of the nanofiber to a few micrometers away. Comparison between experiments and Mie scattering theory allows us to precisely determine the emitter-nanofiber distance and experimental drifts.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
An optical fiber tapered until its diameter is shorter than the wavelength will guide the light in such a way that a significant part of the electromagnetic field spreads outside the surface of the fiber [1, 2]. These modes are both propagating and evanescent, and the non-tapered ends of fibers are readily integrated into optical systems. They have been attracting much interest since the 2000s, for biosensors [3], quantum information [4, 5], coupling light to bigger structures (microspheres [6], photonic crystals [7], microdisks [8], etc.) to quantum emitters (cold atoms [9,10], CdSe quantum dots [11], nitrogen vacancy centers in diamond [12], hBN flakes [13], single molecules [14], etc.). Nanofibers can also be processed [15–17], for instance into nanofiber cavities to enhance the coupling efficiency of an emitter on the surface into its fundamental mode [18]. More than just light wires, nanofibers confine the transverse electromagnetic field to the point that a longitudinal component appears [19], bonding the local polarization of light to its propagation direction; also known as spin-orbit coupling of light [20] or spin-momentum locking [21], this effect opens new possibilites in photonics [22, 23].
The most intuitive way of studying emitters on nanofibers is obviously to excite them through the fundamental guided mode and collect their near-field fluorescence through the same fiber, or their far-field emission in free space. But experimentally, a luminescence background is generated by the optical fiber itself since they are not pure silica (GeO
2doped core, fluorine doped cladding, etc.), and it often spectrally overlaps with the emitter signal. To get rid of this self-fluorescence background, the emitters are often excited sideways, from free space. Under such perpendicular illumination, the nanofiber scatters the incoming light and the excitation field on its surface is the result of interferences. It is crucial to know the spatial distribution of this field if one wants to optimize the emitter excitation.
In this Letter, we report direct observation of these interferences using a scanning fluorescence microscope [24–26]. We probe the intensity of the optical field over a region of 16 × 2 . 3 µm
2with deep sub-wavelength resolution. We compared experimental results to the case of a plane wave scattered by a nanofiber using Mie scattering theory, that provides semi-analytical solution [27]
#346769 https://doi.org/10.1364/OE.27.000350
Journal © 2019 Received 25 Sep 2018; revised 7 Dec 2018; accepted 9 Dec 2018; published 7 Jan 2019
to this problem. Very good agreement between theoretical and experimental data validates our approach for the characterization of the optical field around suspended nanofibers. Moreover, we overcome the experimental challenge to pinpoint a nanoprobe with respect to a suspended nanofiber, leading to λ/ 5 accuracy from near field to far field.
2. Experiment
The experimental setup is described in Fig. 1. A linearly polarized laser ( λ = 568 nm) propagating along the z -axis is focused on the back focal plane of a long working distance objective (numerical aperture NA = 0.70). This produces a collimated beam characterized by a gaussian profile with a full width at half maximum of about 35 µ m. The beam is scattered by a nanofiber ( d = 400 nm, fabricated following reference [28]) suspended in the air along the y -axis. After interaction with the nanofiber, the intensity of the electromagnetic field exhibits fringes generated by the interference between the unscattered and the scattered beam.
xyz piezo
excitation λ = 568 nm
detection λ ≥ 600 nm dichroic
mirror
z y x
fluo. bead Ø100 nm AFM tip
nanofiber Ø400 nm
60×/0.70
Fig. 1. Scheme of our fluorescence scanning probe apparatus. The confocal microscope is focused on a fluorescent bead grafted on the AFM tip. Scanning is done by moving the nanofiber with closed-loop piezoelectric actuators.
In order to directly probe the interference pattern, a fluorescent scanning near-field probe is set above the nanofiber. It consists of a 100 nm dye-doped polystyrene bead grafted on the tungsten tip of an atomic force microscope (AFM) [24]. The fluorescent bead absorbs the incident light and emits a fluorescence signal proportional to the excitation field at its very location (we work well below saturation). Collecting through the same objective used for the excitation, we acquire this emission signal as a function of the nanofiber position relative to the fluorescent probe. The latter must remain immobile in the objective focal plane and is conjugated with a single-photon avalanche diode (PDM-R, Micro Photon Devices [29]) combined with a time-correlated single photon counting system (HydraHarp400, PicoQuant).
Thanks to a xyz piezoelectric scanner, the fiber repeatedly travels 16 µ m back ( x % ) and forth
( x & ) along x by steps of 7.8 nm, then takes a 10 nm step closer to the fluorescent probe in
the z -direction. Our AFM tip vibrates along the x -axis, which coincides with the shear-force
mode [30]. Starting from the largest distance between the nanofiber and the tip, we monitor its
vibration frequency ( f ∼ 32 kHz) and proceed with the xz scan of the fiber, pending contact
between the AFM tip and the nanofiber, which is flagged by a typical shift ∆ f ∼ 2 Hz. Figure
2 shows the first row (Fig. 2(a)) and the last one (Fig. 2(b)) of such a scan. The first contact
occurred during Fig. 2(b), as the nanofiber was moving backward ( x % ). In these graphs, a red square on the scale of x -axis is about 100 nm, like the probe which is the limiting factor on spatial resolution.
0
−2
−4 2 4
x (µm)
∆ 𝒇 (H z)
1
0 2
coun ts /s
0 20 30
10 40
× 103
top row 𝒛 = 2270 nm bottom row 𝒛 = 0 nm
x (µm)
∆ 𝒇 (H z) coun ts /s
× 103
(a) (b)
0
−2 2 4
1
0 2
0 20 30
10 40
−4
0 0.5
−0.5
Fig. 2. Fluorescence signal in counts/s (red squares) and frequency shift ∆ f in Hz (blue dots) along the x -axis, when (a) the tip is z = 2770 nm above the nanofiber, and (b) when we detect the first contact on the nanofiber at z = 0 nm. The inset highlights that the maximum of fluorescence does not coincide with the tip-fiber contact.
Since the scan covers a vertical distance of a few microns, which is much larger than the distance at which shear-force interactions can be detected, the AFM is run without feedback.
It means that we can detect when the AFM tip touches the fiber, but we do not have a reliable measurement of the probe-fiber distance at all times during the xz -scan. This distance will be precisely determined later on. For now, we simply set z = 0 when the first tip-fiber contact occurs while scanning along x , and we scale the rest based on the calibration of the piezoelectric actuator.
Once the fluorescent bead is grafted on the tip, it is necessary to experimentally check its position with respect to the tip apex. This is done by comparing the intensity of the fluorescence signal and the tip vibration frequency close to contact. On the inset of Fig. 2(b), one can measure a δ = 125 nm gap between the maximum fluorescence intensity and the contact point. This is the horizontal deviation from the ideal graft, and it tells us on which side of the tip the fluorescent probe lies. This is of importance, since the tip is tilted (as depicted in Fig. 1): it means that for x < 0 the probe is directly exposed to the light scattered by the nanofiber, whereas for x > 0 the tip end is between the nanofiber and the fluorescent bead.
Another important quantity to be characterized is the vertical distance of the grafting point from the extremity of the tip. Indeed, this distance will define the shorter emitter-nanofiber distance that will be accessible. As we will see later on, a comparison between experimental maps and Mie theory allows a precise determination of the shortest nanofiber-emitter distance achieved in this specific realization of the experiment.
Figure 3 shows experimental (Figs. 3(a) and 3(c)) and theoretical (Figs. 3(b) and 3(d)) maps
of the excitation field intensity in the xz -plane. Due to the geometry of the problem, we studied
two cases: in Figs. 3(a) and 3(b) the laser is polarized parallel to the fiber (along y -axis), and
perpendicular to it (along x -axis) in Figs. 3(c) and 3(d). Experimental maps are obtained by
compiling the x-axis forward scan rows (like in Fig. 2(a)), from far-field (z = 4 λ = 2270 nm)
down to near-field until contact (z = 0 nm). Interferences are clearly visible and the agreement
between theoretical and experimental maps is evident. Note that maps with different polarizations
are plotted with the same intensity range to help with the comparison.
While in the parallel polarized case (Figs. 3(a) and 3(b)) fringes contrast and intensity are high, in the perpendicularly polarized case (Figs. 3(c) and 3(d)), the contrast fades away as the scattering angle and the distance to the fiber increase. Indeed, scattering at large angles means propagating along x after scattering on the fiber. This is unlikely in free space for scattering on a dielectric fiber when the incident polarization is linear along x as well.
Note that fringes contrast and period in the experimental maps are slightly different on each side of the nanofiber. This can be explained by the asymmetry of probe position relative to the apex of the tip, as mentioned when discussing Fig. 2(b).
The keen eye will also notice that around x ∼ 0, the signal ripples along z with a period close to λ/ 2 due to some possible interplay between the tip and the nanofiber forming a Fabry-Perot cavity. It is well known that the presence of the tip is likely to modify the local electromagnetic field (see e.g. [31]). To back this up, on a different set of data (not shown here), we observed that these oscillations are more visible when the tip, nanofiber, and polarization are all parallel to each other.
0 1 2
0
−4
−8 4 8
x (µm)
z (µ m)
5 35 Exp.
0 1 2
z ’ (µ m)
0.5 2.5 |𝑬
𝑦|
2(arb. u.)
0 1 2
z (µ m)
0 1 2
z ’ (µ m)
5 35
0.5 2.5 |𝑬
𝑥|
2(arb. u.) (a)
(b)
(c)
(d)
Theory
Exp.
Theory
⨉
10
3counts/s
⨉
10
3counts/s
Fig. 3. Fluorescence signal over 36 µm
2in the xz-plane; both axes have the same scale. The red dashed circles indicates the nanofiber position. In (a) the excitation beam is polarized parallel to the nanofiber (along y-axis), and in (c) perpendidular to it (along x-axis); pixels are 62 nm wide and 50 nm high (8 × 5 data binning). z = 0 is set when the tip touches the nanofiber and z-axes are scaled using the actuator calibration. Using Mie theory, (b) and (d) show the calculated intensity of the electric field for the same polarizations respectively, this time z
0= 0 is at the surface of the nanofiber.
To take into account the anisotropic scattering produced by the nanofiber, Mie theory is most
suited, given the symmetry of the problem (cylindrical), the ratio of the diameter of the nanofiber
with respect to wavelength (d = 0 . 70 λ ), and the distance range over which we want to know the
optical field (0 to 4 λ ). Semi-analytical solutions [27] are shown in Figs. 3(b) and 3(d) for parallel and perpendicular polarizations, respectively. In this model, an incident plane wave interferes with the optical field scattered by the transparent cylinder (i.e. the nanofiber), which results in a complex set of fringes.
Theoretical calculations need three fixed parameters: the wavelength is set λ = 568 nm; the fiber index is given by its reseller n = 1 . 46; and the diameter of the nanofiber was measured by scanning electron microscopy d = 400 ± 20 nm. The only free parameter that we can adjust to match experimental and theoretical results is the actual emitter-fiber distance, the latter being not continuously measured during the scan with respect to a reference plane as done in standard scanning probe measurements. The experimental z -axis will therefore be corrected by a quantity
∆z that is expected to have two components.
Firstly, a constant one, which was mentioned before: the fluorescent probe is not ideally placed on the apex of the tip. Moreover, the tip cannot hover closer to a suspended nanofiber than a minimum distance below which the fiber suddenly snaps into the tip due to attractive forces between the tip and the fiber which is a soft spring. This situation is rather different to the typical case where the AFM scans on a rigid substrate such as a glass coverslip.
Secondly, a time dependent component: acquiring a 36 µ m
2scan takes sixty minutes, thermal and mechanical drifts are to be expected, be it from the actuators or from the nanofiber stretched in the air.
(a)
0 1 2
𝒛(µm)
0
−2
−4 x(µm) −4 𝚫x−2(µm) 0
0 1 2
𝒛=𝒛′+𝚫𝒛(µm) 0
1 2
0
−2
−4 𝒛=𝒛′(µm)
𝚫x(µm)
0 1 2
0 z(µm)
𝚫z(µm)
0.6